The substrate having the optical surface is, for example, an optical component such as an optical lens or an optical mirror used in optical systems, such as telescopes used in astronomy, or systems used for imaging structures of a mask (“reticle”) onto a radiation sensitive substrate (“resist”) in a lithographic method. The success of such an optical system is substantially determined by the precision with which the optical surface can be machined or manufactured to have a target shape. In such manufacture it is necessary to compare the shape of the machined optical surface with its target shape, and to determine differences between the machined and target surfaces. The optical surface is then further machined at those portions where differences between the machined and target surfaces exceed e.g. a predefined threshold.
Interferometric apparatuses are commonly used for high precision measurements of optical surfaces. Examples of such apparatus are disclosed in U.S. Pat. No. 4,732,483, U.S. Pat. No. 4,340,306, U.S. Pat. No. 5,473,434, U.S. Pat. No. 5,777,741, U.S. Pat. No. 5,488,477, which documents are incorporated herein by reference.
The conventional interferometer apparatus usually includes a reference surface which is illuminated with measuring light, and measuring light reflected back from the reference surface is imaged on a detector. Further, the optical surface to be measured is arranged in a same or separate beam of measuring light, and the optical surface is also imaged on the detector by using light reflected from the optical surface to be measured. The light reflected from the optical surface and the reference surface generate an interference pattern on the detector. By analyzing this pattern, shape differences between the reference surface and the optical surface to be measured can be determined in terms of wavelengths of the measuring light. Thus, the first approach to interferometrically measuring the optical surface allows the determination of the shape thereof only relative to the shape of the reference surface, the shape of which has to be determined by some independent procedure.
The deviation of an optical surface from its target surface is referred to as surface error in the following. The surface errors of an optical surface having a rotationally symmetric target surface may be separated in rotationally symmetric errors and rotationally asymmetric errors. The rotationally asymmetric errors of an optical surface may be absolutely measured according to a method disclosed in the article by R. Freimann et. al., “Absolute measurement of non-comatic aspheric surface errors”, Optics Communications 161 (1996), pages 106 to 114, or as disclosed in US 2002/0063867A1. Here, the term “absolute measurement” means that the determined surface errors are absolute errors rather than relative errors depending on the shape of a reference surface. In this method optical path differences between the surface to be measured and the reference surface of the interferometer are separately measured for plural angular positions with respect to the optical axis of the surface to be measured. The plural measurements are averaged and represent the symmetric surface errors relative to the reference surface. Subtracting the averaged phase differences from the phase differences measured in one particular angular position will then result in a representation of the absolute asymmetric surface errors, however.
There are only few methods known for absolute measurement of rotationally symmetrical surface errors. One such method is illustrated in the article of P. Hariharan, Optical Engineering 36 (9), pages 2478 to 2481, September 1997, using an auxiliary mirror and at least two measuring positions involving high demands on mechanical precision of a measuring apparatus. A further method of such type is disclosed in the article of B. S. Fritz, “Absolute Calibration of an Optical Flat, Optical Engineering 23, page 379, 1984, involving three optical flats and two additional optical wedges of a big size and thermal and mechanical stability.
A method for the determination of the three-dimensional refractive index distribution of a GRIN-lens with plane surfaces is disclosed in US patent application US 2002/0191193 A1.
Further, it is an object of the present invention to provide an improved method for qualifying an optical surface. It is also an object of the present invention to provide an improved method of manufacturing an optical surface.